Question

the north pole is in the middle of the ocean. A person at sea level at the north pole would be 3,949 miles from the center of the earth. The sea floor below the north pole is at an elevation of approximately -2.4 miles. The elevation of the south pole is about 1.7 miles. How far is a person standing on the south pole from a submarine at the sea floor below the north pole?

Answer 1

The distance between a person at the South Pole and a submarine at the sea floor below the North Pole is 7,897.3 miles, considering the given Earth radius and the elevations of the poles.

Step-by-step explanation:

To find the distance between a person standing at the South Pole and a submarine at the sea floor below the North Pole, we can consider the Earth's radius and the elevations at both poles. The radius of the Earth at the North Pole is given as 3,949 miles. The elevation of the sea floor below the North Pole is given as -2.4 miles below sea level, which means the submarine is 3,949 - 2.4 = 3,946.6 miles from the center of the Earth. The elevation of the South Pole is given as 1.7 miles above sea level, therefore a person standing at the South Pole is 3,949 + 1.7 = 3,950.7 miles from the center of the Earth.

To find the distance between these two points, we can use the spherical distance formula, which, simplified for opposite points on a sphere (which the North and South Poles are), is the sum of the distances of each point from the center of the sphere. Thus, the distance between the person at the South Pole and the submarine at the North Pole is 3,950.7 + 3,946.6 = 7,897.3 miles.

Answer 2

7,897.30 miles

Step-by-step explanation:

It is given that the North Pole is at a distance of 3,949 miles from the center of the earth.

We also know that the sea floor is below 2.4 miles from the sea level.

It is given that a submarine is located at the sea floor near North Pole. Hence, the distance of the submarine from the center of the earth would be

3949 - 2.4 = 3946.6 miles.

On the other hand, the South Pole is given to be at an elevation of 1.7 miles from the sea level.

Since we know that the sea level is at a distance of 3949 miles from the center of the earth, we can immediately calculate the distance of the South Pole from the center of the earth to be

3949 + 1.7 = 3950.7 miles.

Putting all of this together, we see that the center of the earth is at a distance of 3946.6 miles from the submarine near the North Pole, and the center of the earth in turn is 3950.7 miles from the South Pole.

Hence, the distance between the submarine and a person on the South Pole = 3946.6 + 3950.7 = 7897.3 miles.